On the third day of star-mapping (with Lt. Bailey as navigator in place of Ensign Chekov), the Enterprise discovers a giant multi-colored spinning cube. McCoy, who is giving Kirk his quarterly medical examination, fails to inform Kirk about the crisis, quipping (to himself) ``If I jumped every time a light went off around here, I'd end up talking to myself.'' As a result of the exam, Kirk's diet is restricted to salad, much to his chagrin. The cube, which holds a distance of 1593 m, is 107 m on an edge, and > 11,000 metric tons in weight, has an unknown propulsion system which prompts Scotty to admit that it ``beats me what makes it go.'' As the Enterprise tries to maneuver away from the cube, the cube begins emitting deadly radiation and Kirk is forced to destroy it.
Responding to the destruction of what turns out to have been a warning buoy, a mile-diameter spherical flagship known as the Thesarius rushes to the scene. It is piloted by Balok and belongs to the First Federation. Balok threatens to destroy the Enterprise for violating First Federation space and destroying the warning buoy. Balok gives the crew of the Enterprise 10 minutes to consult with their deity before they are destroyed. Prompted by uncharacteristic curiosity, Spock is able to obtain a visual image of the imposing Balok using the ship's monitor during this waiting period.
Kirk saves the day by pretending that the Enterprise is equipped with a secret ``corbomite device'' capable of destroying any vessel which attacks it. Balok then offers to spare the crew of the Enterprise by towing it to a First Federation planet, interning the crew there, and only then destroying the Enterprise. However, Kirk waits for the tow ship to expend its power, then pulls away, crippling the power systems of the tow ship.
Kirk, McCoy, and Dave Bailey transport to the main ship Thesarius to render assistance. Here, they meet Balok, the pilot of the ship, who greets them and offers them ``tranya'' to drink. Kirk and company find that the image of Balok they had glimpsed was a phony puppet and that Balok is actually an unintimidating midget. It turns out that Balok did not trust the information he gleaned from his scan of the Enterprise's data banks and was simply testing the Earth men to see what their true intentions were. Bailey, who had panicked during the crisis on the bridge of the Enterprise, remains on the Thesarius to exchange cultures with Balok after a tour of the Thesarius by Balok.